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Hi Arbitrageur

I wanted to ask you a question about the Schiehallion Experiment

The Schiehallion experiment was an 18th-century experiment to determine the mean density of the Earth. Funded by a grant from the Royal Society, it was conducted in the summer of 1774 around the Scottish mountain of Schiehallion, Perthshire. The experiment involved measuring the tiny deflection of a pendulum due to the gravitational attraction of a nearby mountain. Schiehallion was considered the ideal location after a search for candidate mountains, thanks to its isolation and almost symmetrical shape. One of the triggers for the experiment were anomalies noted during the survey of the Mason–Dixon line.

the background on the experiment , one particular part I'd be grateful if you could explain it to me

A pendulum hangs straight downwards in a symmetrical gravitational field. However, if a sufficiently large mass such as a mountain is nearby, its gravitational attraction should pull the pendulum's plumb-bob slightly out of true (in the sense that it doesn't point to the centre of mass of the Earth).

Why is the mountain itself considered an external body of mass to the mass of the earth , if the mountain is actually a part of the earth itself.

Isn't the mass of the mountain itself also considered as a part of the total mass of the earth when calculating the total mass of the earth ?

Is this to do with the centre of the mass of the mountain not being the centre of mass of the earth and so you can use them as independent variables ?

I have read further and I think that I understand the premise that it explains

If the mass of the mountain could be independently established from a determination of its volume and an estimate of the mean density of its rocks, then these values could be extrapolated to provide the mean density of the Earth, and by extension, its mass.

I was just trying to figure out how it was done and I think I understand it now hahaha

a reply to: sapien82
It sounds like you figured it out. The diagram at your source is helpful.

If you're far enough away from the Earth, say on the moon, it's a good approximation to treat the mountain and the Earth as part of one mass centered at the center of mass of the Earth. It's only as you get closer to the Earth where the angle to the center of mass of the Earth and the center of mass of the mountain start diverging significantly, and in the illustration at your source that angle is shown as approximately 90 degrees though in comparing measurements on either side of the mountain they had to account for the curvature of the Earth, so they didn't use exactly 90 degrees.

I didn't realize that experiment prompted the invention of contour lines until I read the article. They used those to aid is calculating the mass of the mountain.

I'd love to see the equipment they used in 1774 to make such precise measurements. Newton's objection to the experiment was that he didn't think the measurements could be made accurately enough because there are very small angles involved which aren't easy to measure, but I suspect Newton would have been impressed with what a good job they did in 1774 making those measurements. Their calculation of the density of the Earth was a bit low but still impressive given the difficulty of making such precise measurements with the equipment available.

a reply to: Arbitrageur

Hey thanks mate , I really appreciate it.

It looks as though they repeated the experiment in 2005 via three scientists working for a company out of Glasgow

Weight of the world challenge

a reply to: sapien82
You're welcome. Yes they got much closer to the "modern value" for density of the Earth on the latest measurement in 2005 compared to the 1774 measurement, and there were some other measurements in between. The 2005 model of the mountain was more complex to include known density variations and had a more accurate shape, and the angle measurements were more accurate. This was the result published in 2007:

Maskelyne’s 1774 Schiehallion experiment revisited

Nevil Maskelyne’s 1774 experiment on the Scottish mountain Schiehallion set out to derive the mean density of the Earth, from astronomical observations of the deflection of the vertical and calculation of the mountain’s relative gravitational attraction. Using Maskelyne’s results and lithological survey results, John Playfair estimated mean Earth specific gravity to be 4.56–4.87, while Charles Hutton argued in 1821 that the Earth was ‘very near five times the density of water; but not higher’. Hutton challenged future workers to identify any areas in which his analysis could be improved. The geometry of the 1774 experiment has therefore been recomputed within a digital elevation model extending 120 km from the mountain. Three contributions to the deflection of the vertical have been included: topography, and local and regional subsurface density variations. Local subsurface densities have been modelled using geological maps, cross-sections and laboratory measurements. Regional subsurface effects have been included from analysis of the Bouguer gravity anomaly. The outcome of the new modelling is to credit Maskelyne for his accurate astronomical observations, as together with the new density structure model, they yield a mean Earth density of 5480 ± 250 kgm^−3, in agreement with the modern value of 5515 kg m^−3.

a reply to: Arbitrageur

it's amazing that in 1774 a team of scientists and laborers worked for 17 weeks on a monroe in Scotland to weight the world!

Im amazed , I wanted to go to Schiehallion and maybe even attempt to repeat the experiment , would make for a nice summer holiday.

I will see if the royal society has any further information on the equipment they used.
But from what I can tell they used normal equipment for the time
pendulum , telescopes, levels , I think the only device that maybe tricky is the angle measurement
and i'd likely end up using a theodolite

don't you think its amazing that through the task of surveying that Hutton invented contour lines

GENIUS !

This is a really simple and basic question. I am about seem very stupid but i rather ask and learn, than stay stupid.

Isn't heat always just heat, regardless of the heat source? Are there different kinds of heat?

Google told me that "conduction in solids, convection of fluids (liquids or gases), and radiation through anything that will allow radiation to pass. The method used to transfer heat is usually the one that is the most efficient." And that is about transfer. But the heat which is transferred is always the same thing right?

I like sauna very much. Electric saunas don't feel as good as the ones with the wood burning stove. I have an electric heater in my sauna, stones of course, and when i throw water on the stones, the result is not as pleasant as with wood burning stoves. Sometimes i get to bathe in a wood burning stove sauna, they are usually near a lake or sea, beautiful scenery, trees, nature. So my thought has always been that heat is heat, there is one heat, and that's it, and saunas in nature, with wood burning stoves and water nearby, just make the overall experience so much more pleasant that the heat feels better there too.

originally posted by: sapien82
don't you think its amazing that through the task of surveying that Hutton invented contour lines

GENIUS !

Yes, I think the entire experiment was amazing for 1774 technology. I always took contour lines for granted and never even thought about how they were first invented or used.

originally posted by: Finspiracy
This is a really simple and basic question. I am about seem very stupid but i rather ask and learn, than stay stupid.

When I watched these Veritasium videos, I realized that probably most people don't understand heat versus temperature and have some misconceptions about both, so I recommend watching these if you can since they try to correct some misconceptions. Watching both will take less than 10 minutes:

Misconceptions About Heat


Misconceptions About Temperature

Isn't heat always just heat, regardless of the heat source? Are there different kinds of heat?

Google told me that "conduction in solids, convection of fluids (liquids or gases), and radiation through anything that will allow radiation to pass. The method used to transfer heat is usually the one that is the most efficient." And that is about transfer. But the heat which is transferred is always the same thing right?

Google told you right, but it doesn't say it's always the same thing exactly, does it? It talks about different types of heat transfer, and even if you pick one type like conduction in solids, that transfer can vary dramatically from one type of solid to another type of solid, as demonstrated in the veritasium video, enough to throw off our perceptions of heat and temperature enough that nearly everybody gets the wrong answers to what is going on in the demonstrations. That video shows people touching a book and touching a hard drive, and the thermal conductivity of those solids is so much different that people have a hard time judging the temperatures of them by touching them. When Derek says they are the same temperature, everybody calls him a liar until he proves it using a thermometer.

People think the metal object is colder than the non-metal object, but it's not, they are the same temperature. The metal feels colder because it conducts heat away from your hand more quickly.

I like sauna very much. Electric saunas don't feel as good as the ones with the wood burning stove. I have an electric heater in my sauna, stones of course, and when i throw water on the stones, the result is not as pleasant as with wood burning stoves. Sometimes i get to bathe in a wood burning stove sauna, they are usually near a lake or sea, beautiful scenery, trees, nature. So my thought has always been that heat is heat, there is one heat, and that's it, and saunas in nature, with wood burning stoves and water nearby, just make the overall experience so much more pleasant that the heat feels better there too.

I have no idea how to explain that using physics, but if you're suggesting the answer is psychological because you prefer the beauty of nature, that would make sense.

a reply to: Finspiracy

I think I Understand what you mean about the difference between the heat , what I think is a dry heat and heat with humidity in the air give you very different feelings in the body on your skin.

I prefer humid heat to dry heat , like the heat of a forest or jungle , compared to the heat of a desert.

a reply to: Arbitrageur

and to think in 1774 it was only 19 years after the last jacobite rebellion in Scotland.
Im amazed at even though we war and fight , humans are still holding the torch aloft
keeping the light of truth shining and to illuminate us all with knowledge and understanding, rather than division.

The world surely is a very strange place.

a reply to: Arbitrageur

Thank you for your answer, it helped me to correct some bad misconceptions i had about heat and temperature. But i was not clear enough with my question to begin with. I will continue on the basis of the reply of sapien82.

originally posted by: sapien82
a reply to: Finspiracy

I think I Understand what you mean about the difference between the heat , what I think is a dry heat and heat with humidity in the air give you very different feelings in the body on your skin.

I prefer humid heat to dry heat , like the heat of a forest or jungle , compared to the heat of a desert.

Yes, this has to do with humidity too, and the heat which is stored into the material (stones this time) to create steam. All of us here are told at a very young age, that the temperature of a sauna does not increase when water is thrown on the stones, which are on the sauna stove. Like... you can be in a 100 degree (celsius) air for a while but never in a water that hot. It is the humidity that increases with water -> steam reaction. But the body sensation is heat.

And the result of that water -> steam reaction feels different in an electric sauna, when compared to a one with a wood burning stove. And i have a long time been wondering why is that, if heat is always heat?

a reply to: Finspiracy

And i have a long time been wondering why is that, if heat is always heat?

Heat is always heat but our perception of it depends on the transfer of heat.

A number of years ago I was visiting relatives in Tucson. In September. It was really, really hot. But it was "dry heat." My relatives had a swimming pool which I took full advantage of. It felt great. Until I got out of the pool, where upon I felt really cold. Cold to the point of shivering.

See, what was happening was the water on my skin was evaporating very rapidly because of the combination of a high temperature (atmospheric heat) and low humidity. That resulted in heat being drawn out of my skin (due to the phase change of water to gas) and a feeling of cold even though the temperature was high.

If the humidity were higher the water on my skin would not have evaporated as rapidly and the cooling effect would not have occurred. I would have gotten out of the pool and felt...warm.

originally posted by: Finspiracy
Yes, this has to do with humidity too, and the heat which is stored into the material (stones this time) to create steam. All of us here are told at a very young age, that the temperature of a sauna does not increase when water is thrown on the stones, which are on the sauna stove. Like... you can be in a 100 degree (celsius) air for a while but never in a water that hot. It is the humidity that increases with water -> steam reaction. But the body sensation is heat.

And the result of that water -> steam reaction feels different in an electric sauna, when compared to a one with a wood burning stove. And i have a long time been wondering why is that, if heat is always heat?

The reason I didn't think humidity should explain the difference between the electric sauna versus wood-burning is because the exhaust gases from burning wood, while containing water vapor, should be vented outside the sauna, so that shouldn't have an effect. So if you put water on the heated stones to create humidity, if everything else is the same, such as the type of stones, temperature of the stones, amount of water used, etc, then the amount of humidity generated from putting water on the stones should be the same either way, shouldn't it?

If the temperature and or humidity are not the same, then they may not feel the same. What I would suggest is getting an inexpensive combination temperature/humidity gauge and take it into both saunas and measure the temperature and humidity in each, so you can see what is different.

The reason humidity affects our perception of heat is that our bodies cool through perspiration, and this has less cooling effect in humid air than in dry air. If the air is already saturated with moisture, not as much of your perspiration can evaporate and cool you off. This concept is the origin of the so-called "heat index" you've probably heard the weatherman talking about, when he says it's 95 degrees outside but feels like 100 (because of the humidity), though that may not be completely accurate for every person since it makes assumptions about your size and amount of clothing, but it does give you some idea of the perceptual difference to expect.

Why exactly perspiration cools us off is also an interesting topic but I'm not sure if that's part of your question or not.

a reply to: Phage

I agree with your answer and i appreciate your knowledge as i always do. But my question applies solely and exclusively to a sauna.

originally posted by: Arbitrageur
So if you put water on the heated stones to create humidity, if everything else is the same, such as the type of stones, temperature of the stones, amount of water used, etc, then the amount of humidity generated from putting water on the stones should be the same either way, shouldn't it?

Yes

But it feels so different. Thanks for all the replies fine folks. I am going to my sauna now (electric one, unfortunately)

a reply to: Finspiracy

The venue is irrelevant.

The point is that our perception of heat is not directly related to temperature. This fact does not address the question of subjectivity.

a reply to: Finspiracy
There could be another variable, also related to evaporation. Saunas often have ventilation systems that exchange the air, and the amount of air flow can also affect the evaporation rate of perspiration, in addition to temperature and humidity, so consider that also.

Three months have passed, so it is time to chime in with a post on aetherial matters...

originally posted by: delbertlarson
a reply to: Arbitrageur

The aether work resumed in mid March...The new approach involves only three very simple postulates and an assumed fermionic, continuous, two-component aether. The postulates are: 1) The density of negative-aether always equals the density of positive-aether; 2) A flow force is proportional to absolute flows and proportional to the detached-aether density; 3) A tension is proportional to the aetherial separation within a quanta, plus whatever is required to offset any externally applied force. From that underpinning the individual parts of Maxwell's Equations and the Lorentz force equation are derived in about 60 pages, double spaced. While all pieces are now done, there is still a need to integrate the document, clean it up and review it. Unfortunately, that process often unearths an issue that can set things back. But progress is being made.

As typically happens, my aether model once again had problems upon further analysis shortly after my June post quoted above. The June version proposed forces due to absolute flows, and really, if there is a flow force it should be relative. (If A flows through B at speed v, or if B flows through A at speed -v, one would expect the force to be the same.) I have now come up with a pair of postulates that enable more satisfactory flow laws. For the first time, I have an integrated write-up that got all the way to both Maxwell's Equations (ME) and the Lorentz Force Equation (LFE) from a pretty simple physical model. The model is really not too different from normal solid matter, as both the aether and normal solids have a positive and negative component, and both the aether and normal solids are described well by quantum mechanics. The only new additions are a few rather simple postulates regarding density equality, tension and flows. I have begun working through a careful review of the present draft, and while there is a real possibility I will find some error to once again derail things, as of now I remain optimistic that I finally have the desired unified derivation of ME and LFE from aetherial underpinnings.

However there is a new issue that could further delay publication. Quite a while ago I realized that the aether may be dark matter. I checked around a bit and found that the missing mass needed for dark matter is about equal to the mass of two electrons per liter, or, one electron and one positron per liter. If we propose that the negative (positive) aether component is made of electrons (positrons) under a state change, that would infer a single charge per liter as the aether density for each component. My present derivation assumes that the aether density is much greater than the charge density of the proton, which is in conflict with an aether of one charge per liter. Now, the aether may be comprised of particles far lighter than the electron, and/or also, the derivation could possibly be done without my density assumption, and while I've looked a bit into that, completing such a study and writing it up will take additional time. The present plan is to complete the present derivation of ME and LFE first. Once that is complete and carefully checked to be correct, the aetherial density and dark matter questions can be investigated.

a reply to: delbertlarson

Nice to see you're still making progress.

I hope you can sort out the problems that may crop up.

You have mentioned something there which may help you.

Quite a while ago I realized that the aether may be dark matter.

I think the main issue with your model is the name Aether.

It's off-putting. Sorry. But, weather true or false. People don't like it.

I don't agree that it's Dark Matter.

I would say it's Dark Energy though. And is intrinsic to the universe. Which is what you describe.

Dark Matter would be an interaction of the D/E. Causing a particle D/M. And possibly other matters which would probably all be considered D/M at this stage. But. There could be more than one type of D/M. But that's only my opinion.

And, as it is only a placeholder anyway. Time moves on and names change. Even though the thing it is remains the same. I don't see how changing the name of your model to keep up with the times would harm it. Perhaps it would be more helpful.

a reply to: delbertlarson
a reply to: blackcrowe

blackcrowe, I can't agree with a lot of what you said, but if I had to make a choice of whether hypothesized luminiferous aether was more like dark matter or dark energy, I would have to go with dark energy, not so much for the reason you mention which I don't understand, but because I would imagine that if such an aether existed it would probably be distributed somewhat uniformly and with our limited understanding of dark energy so far, it seems to be uniformly distributed.

In contrast, dark matter is certainly not uniformly distributed. Scientists have even mapped the density variations using gravitational lensing observations:

Unprecedentedly wide and sharp dark matter map

So as that map shows we see dramatic variations in apparent dark matter density.

Why do I think this may be an issue for luminiferous aether?

When we have waves propagating in other media, as the properties of the medium vary, the wave propagation through that medium also varies.

For example, as the density of air varies in Earth's atmosphere, so does the speed of sound waves, and the speed of sound in water varies based on temperature, salinity and pressure/depth. So if the density of dark matter is varying that might be a problem for the dark matter being a medium for light to travel through at a constant speed, if the density variations had an effect on the speed as happens in other examples we know of for other types of waves and media.

I'm not trying to suggest that dark energy could be luminiferous aether, only that I see it as more similar to aether based on the above than dark matter. I'm ok with no medium being needed to propagate light and the likelihood that no luminiferous aether exists, but on the other hand I don't think such aether has been conclusively proven false, so I try to keep an open mind.